For comparison, an adult GA is CHF 3860/yr, so paying for a parking space in Zürich alone puts you 2/3rd of the way to the cost of public transportation, even disregarding costs like insurance, the car itself, registration, vignette, fuel, vehicle maintenance, tyres and parking costs away from home.
It's CHF 300 per year in a blue zone where you have to find a spot whenever you feel like parking your car.
If you have vacant spaces in blue zones near you, that's a viable option. There are plenty of places where that's not the case though.
[0]: https://www.immoscout24.ch/de/parkplatz/mieten/ort-zuerich
A first class Generalabonnement is virtually half the price of that.
So, no. It's certainly not cheaper to drive.
If you Google the question you find a variety of answers, but I think looking at it from the tax man's perspective is a good start.
I agree that the cost nay vary, but it can also be significantly higher than 1K per month, depending on the model of car, yearly kilometers and your risk from an insurance perspective.
[0] That's the rate you can deduct from your taxable income per kilometer if you use a private car for work purposes.
I don't know about prices now, but when I lived there, if you actually needed to travel so much that the GA was worth it over the half-fare card, it definitely was worth it over the car, just on gas prices alone.
So at least comparing to NL, public transport in CH is brutally cheap.
Owning a car is brutally expensive.